#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
宇宙数学工具
提供道AI专用的数学函数和工具
"""

import paddle
import paddle.nn as nn
import numpy as np
from typing import Tuple, Optional
import math

class CosmicMath:
    """宇宙数学工具类"""
    
    @staticmethod
    def quantum_entanglement(state1: paddle.Tensor, state2: paddle.Tensor) -> paddle.Tensor:
        """量子纠缠计算"""
        # 张量积创建纠缠态
        entangled = paddle.outer(state1, state2)
        
        # 全息压缩
        compressed = CosmicMath.holographic_compression(entangled, state1.shape)
        
        return compressed
    
    @staticmethod
    def holographic_compression(large_state: paddle.Tensor, target_shape: Tuple) -> paddle.Tensor:
        """全息压缩算法"""
        # 重塑为矩阵
        matrix_form = large_state.reshape([-1, large_state.shape[-1]])
        
        # 奇异值分解
        U, s, Vh = paddle.linalg.svd(matrix_form, full_matrices=False)
        
        # 保留主要成分
        k = min(target_shape[-1], len(s))
        compressed = paddle.matmul(U[:, :k], paddle.diag(s[:k]))
        
        return compressed.reshape(target_shape)
    
    @staticmethod
    def calculate_cosmic_alignment(state: paddle.Tensor) -> float:
        """计算宇宙校准度"""
        # 计算信息熵
        prob_dist = nn.functional.softmax(state, axis=-1)
        entropy = -paddle.sum(prob_dist * paddle.log(prob_dist + 1e-8))
        
        # 最大可能熵
        max_entropy = math.log(state.shape[-1])
        
        # 校准度 = 1 - 归一化熵
        alignment = 1.0 - (entropy / max_entropy).item()
        return max(0.0, min(1.0, alignment))
    
    @staticmethod
    def yang_yin_balance(yang_force: paddle.Tensor, yin_force: paddle.Tensor) -> Dict:
        """计算阴阳平衡度"""
        yang_norm = paddle.norm(yang_force).item()
        yin_norm = paddle.norm(yin_force).item()
        
        ratio = yang_norm / (yin_norm + 1e-8)
        
        if 0.9 <= ratio <= 1.1:
            status = "完美平衡"
            score = 1.0
        elif 0.7 <= ratio <= 1.3:
            status = "良好平衡"
            score = 0.8
        elif 0.5 <= ratio <= 1.5:
            status = "基本平衡" 
            score = 0.6
        else:
            status = "失衡状态"
            score = 0.3
        
        return {
            'status': status,
            'score': score,
            'ratio': ratio,
            'yang_strength': yang_norm,
            'yin_strength': yin_norm
        }
    
    @staticmethod
    def fractal_dimension_estimation(state: paddle.Tensor, num_scales: int = 10) -> float:
        """估计分形维度"""
        norms = paddle.abs(state)
        max_norm = paddle.max(norms).item()
        
        scales = np.linspace(0.1, 1.0, num_scales)
        counts = []
        
        for scale in scales:
            threshold = scale * max_norm
            count = paddle.sum(norms > threshold).float().item()
            counts.append(count)
        
        if len(counts) < 2:
            return 1.0
        
        # 对数线性回归
        log_scales = np.log(1 / np.array(scales))
        log_counts = np.log(np.array(counts) + 1e-8)
        
        # 简单线性拟合
        if np.std(log_scales) < 1e-8:
            return 1.0
            
        fractal_dim = (log_counts[-1] - log_counts[0]) / (log_scales[-1] - log_scales[0])
        return float(fractal_dim)
    
    @staticmethod
    def cosmic_distance(state1: paddle.Tensor, state2: paddle.Tensor) -> float:
        """计算宇宙距离（余弦相似度的补数）"""
        similarity = nn.functional.cosine_similarity(state1, state2).item()
        distance = 1.0 - similarity
        return max(0.0, distance)
    
    @staticmethod
    def wisdom_entropy(state: paddle.Tensor) -> float:
        """计算智慧熵值"""
        # 使用多种熵度量
        prob_dist = nn.functional.softmax(state, axis=-1)
        
        # Shannon熵
        shannon_entropy = -paddle.sum(prob_dist * paddle.log(prob_dist + 1e-8)).item()
        
        # Renyi熵 (α=2)
        renyi_entropy = -paddle.log(paddle.sum(prob_dist ** 2)).item()
        
        # 综合熵值
        combined_entropy = (shannon_entropy + renyi_entropy) / 2
        
        return combined_entropy

class ComplexCosmicMath:
    """复杂宇宙数学工具"""
    
    @staticmethod
    def quantum_taiji_transform(state: paddle.Tensor, iteration: int) -> paddle.Tensor:
        """量子太极变换"""
        # 创建复数状态
        complex_state = paddle.complex(state, paddle.roll(state, shifts=1, axis=-1))
        
        # 量子相位旋转
        phase = 2 * math.pi * iteration / 3  # 三生万物
        rotated = complex_state * paddle.complex(
            paddle.cos(phase), paddle.sin(phase)
        )
        
        # 返回实部作为变换结果
        return paddle.real(rotated)
    
    @staticmethod
    def holographic_fourier_analysis(state: paddle.Tensor) -> Dict:
        """全息傅里叶分析"""
        # 傅里叶变换
        fourier_transform = paddle.fft.fft(state)
        
        # 频谱分析
        magnitude_spectrum = paddle.abs(fourier_transform)
        phase_spectrum = paddle.angle(fourier_transform)
        
        # 主要频率成分
        dominant_freq = paddle.argmax(magnitude_spectrum).item()
        spectral_entropy = CosmicMath.wisdom_entropy(magnitude_spectrum)
        
        return {
            'dominant_frequency': dominant_freq,
            'spectral_entropy': spectral_entropy,
            'total_energy': paddle.sum(magnitude_spectrum).item(),
            'phase_coherence': paddle.std(phase_spectrum).item()
        }
    
    @staticmethod
    def multidimensional_correlation(states: List[paddle.Tensor]) -> paddle.Tensor:
        """多维相关性分析"""
        if len(states) < 2:
            return paddle.to_tensor(1.0)
        
        # 构建相关矩阵
        n_states = len(states)
        correlation_matrix = paddle.zeros([n_states, n_states])
        
        for i in range(n_states):
            for j in range(n_states):
                if i == j:
                    correlation_matrix[i, j] = 1.0
                else:
                    corr = nn.functional.cosine_similarity(
                        states[i].unsqueeze(0), 
                        states[j].unsqueeze(0)
                    ).item()
                    correlation_matrix[i, j] = corr
        
        return correlation_matrix

class CosmicOptimizer:
    """宇宙优化器"""
    
    def __init__(self, parameters, learning_rate: float = 1e-4):
        self.optimizer = paddle.optimizer.Adam(
            learning_rate=learning_rate,
            parameters=parameters,
            beta1=0.9,
            beta2=0.999,
            epsilon=1e-8
        )
        
        self.cosmic_scheduler = paddle.optimizer.lr.CosineAnnealingDecay(
            learning_rate=learning_rate,
            T_max=100
        )
    
    def cosmic_step(self, loss: paddle.Tensor):
        """宇宙优化步骤"""
        loss.backward()
        
        # 梯度裁剪（防止宇宙爆炸）
        paddle.nn.utils.clip_grad_norm_(
            self.optimizer._parameter_list, 
            max_norm=1.0
        )
        
        self.optimizer.step()
        self.optimizer.clear_grad()
    
    def adjust_cosmic_learning_rate(self, alignment: float):
        """根据宇宙校准度调整学习率"""
        if alignment > 0.8:
            # 高校准度，小幅调整
            new_lr = self.cosmic_scheduler.get_lr() * 0.95
        elif alignment < 0.5:
            # 低校准度，需要更大学习率
            new_lr = self.cosmic_scheduler.get_lr() * 1.1
        else:
            # 中等校准度，保持稳定
            new_lr = self.cosmic_scheduler.get_lr()
        
        self.cosmic_scheduler.step()